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Foreign object damage and fatigue crack threshold

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International Journal of Fracture 107: 31–51, 2001.© 2001 Kluwer Academic Publishers. Printed in the Netherlands.Foreign object damage and fatigue crack threshold: Crackingoutside shallow indentsXI CHEN and JOHN W. HUTCHINSONDivision of engineering and applied sciences, Harvard university, Cambridge, MA 02138, USAReceived 23 November 1999; accepted in revised form 9 June 2000Abstract. Foreign Object Damage (FOD) usually happens when objects are ingested into jet engines poweringmilitary or civil aircraft. Under extreme conditions, FOD can lead to severe structural damage. More commonlyit produces local impacted sites of the fan and compressor airfoils, lowering fatigue life of these components.FOD is a prime cause for maintenance and repair in aircraft engines. In this paper, a framework for analyzingFOD and its effect on fatigue cracking is established. A finite element analysis is used to identify three relevantregimes of FOD related to the depth of penetration into the substrate, and to determine the residual stresses. Mostof the emphasis in this paper focuses on fatigue cracks emerging from shallow indentations, which are generallyexpected to be of most practical concern. Full three-dimensional finite element solutions are obtained for semi-circular surface cracks emerging from specific locations at the indentation revealing the influence of the residualstress on the stress intensity factor distribution. For shallow indents, a relatively simple dimensionless formula forthe relation between the residual stress intensity factor, the crack size, and the indentation width are developed.These results, together with results for the intensity factor variations due to cyclic loading, have been used toaddress the question: To what extent do the residual stresses caused by the FOD reduce the critical crack sizeassociated with threshold fatigue crack growth? Formulas for the critical crack size are obtained. Specific resultsare presented for the blade alloy, Ti-6Al-4V, revealing that FOD can reduce the critical crack size by as much as60%.Key words: Foreign object damage, contact mechanics, crack mechanics, fatigue analysis, indentation regimes,critical crack size.1. IntroductionForeign object damage by hard-particles mainly occurs during motion of the aircraft on theairfield, during takeoff and during landing. Typical objects ingested are stones and other debrisfrom the airfield, with sizes in the millimeter regime. Typical impact velocities are in the rangeof 100 - 350 m/s, depending on the specific engine. Of concern here are impact locationson the blades. Such microstructural damage can promote fatigue-crack growth under high-cycle fatigue loading. This has become a critical issue in the lifetime prediction of turbine-engine components and a prime concern in maintenance and repair (Ritchie et al., 1999; Peterset al., 2000). The unusually high frequencies typical of in-flight vibratory loading necessitate adefect-tolerant approach based on designing below the threshold for fatigue crack propagation.FOD damage must be factored into this approach. Otherwise, the FOD damage can lead tonon-conservative life prediction and unexpected high-cycle fatigue failures.Most FOD occur as damage to the leading edges of turbine blades. To gain insight intothe interaction between FOD and fatigue cracking, we have considered a less frequent formof FOD whereas the damage is assumed to occur away from the edge. The research has beencoordinated with a parallel experimental study (Peters et al., 2000). The study initiated in32 Xi Chen and John W. HutchinsonFigure 1. The geometry of spherical indentation.Figure 2. A semi-circular surface crack with radius a is embedded inside the residual stress field of the indent andsubjected to cyclic stress σ(t).this paper considers the normal impression of a hard spherical particle into a thick elastic-plastic substrate (Figure 1). The indentation field is axisymmetric. The resulting residualstresses are determined and the locations at the surface where tensile stresses are most likelyto promote cracking are identified. The second step in the approach is the three-dimensionalfinite element analysis of a semi-circular surface crack within the residual stresses field. Thefinal step combines the stationary stress intensity factor due to the indent with the intensityfactor variation due to the cyclic loads (Figure 2) to make predictions for critical crack sizesbased on threshold fatigue crack growth data.The parallel experimental study has been conducted by Peters et al. (2000), who investi-gated the influence of FOD on the high-cycle fatigue properties of Ti-6Al-4V alloy, whichis commonly used as gas turbine blades in military aircraft. The material is almost ideallyplastic with very little strain hardening and a tensile yield stress of about 950 MPa. In theirexperiments, they used hardened steel spheres (with diameter 3.175 mm) to normally impacta flat Ti-6Al-4V alloy specimen at 200–300 m s−1. After impact, the specimens were cycled ata maximum nominal stress of 500 MPa at a load ratio of 0.1, and the initiation and subsequentgrowth of the fatigue cracks emerging from the indent were observed. The authors found thatFOD provides sites for the initiation of small fatigue cracks, and in some cases crack initiationoccurred at cycle lifetimes which were orders of magnitude lower than found for un-impactedspecimens. For the 200 m s−1impact, crack initiation was observed to occur at the bottom ofthe indent, while the 300m/s impact a prominent crater rim was produced and this turned outto be the site of the crack initiation.The paper is organized by sections to follow the three steps mentioned in connection withthe overall approach. Section 2 presents the indentation analysis and results. Here contact ismade with recent work on the finite element analysis of indentation. In particular, it will beseen that three separate regimes to the indentation problem can be identified: very shallow,moderately shallow and deep indents. The primary focus in this paper will be on moderatelyshallow indents for which relatively simple scaling relations exist for the residual stress fields.Some discussion of trends for deep indentations will also be given. The solutions for thestress intensity factor for a semi-circular surface crack within the residual stress field of theForeign object damage and fatigue crack threshold 33Figure 3. The indentation map from Mesarovic and Fleck


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